On the Effective Region of Convergence of the Decomposition Series Solution
In this paper we investigate the domain of convergence of the Adomian series solution based on the computational results for several examples. We demonstrate how the domain of convergence can be extended by introducing a parameter c in the definition of the zeroth-order and first-order solution comp...
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SAGE Publishing
2013-06-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/1748-3018.7.2.227 |
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doaj-4830fc6e163f49aebf1de984a32d65352020-11-25T03:44:02ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262013-06-01710.1260/1748-3018.7.2.227On the Effective Region of Convergence of the Decomposition Series SolutionJun-Sheng Duan0Randolph Rach1Zhong Wang2 College of Science, Shanghai Institute of Technology, Shanghai 201418, P.R. China 316 South Maple Street, Hartford, Michigan 49057-1225, U.S.A. School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong 526061, P.R. ChinaIn this paper we investigate the domain of convergence of the Adomian series solution based on the computational results for several examples. We demonstrate how the domain of convergence can be extended by introducing a parameter c in the definition of the zeroth-order and first-order solution components u 0 and u 1 . Furthermore we generalize the concept of the convergence parameter c from a two-term partition of the initial condition to a multiple-term partition with the design of expanding the domain of convergence of the Adomian series solutions for nonlinear differential equations.https://doi.org/10.1260/1748-3018.7.2.227 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jun-Sheng Duan Randolph Rach Zhong Wang |
| spellingShingle |
Jun-Sheng Duan Randolph Rach Zhong Wang On the Effective Region of Convergence of the Decomposition Series Solution Journal of Algorithms & Computational Technology |
| author_facet |
Jun-Sheng Duan Randolph Rach Zhong Wang |
| author_sort |
Jun-Sheng Duan |
| title |
On the Effective Region of Convergence of the Decomposition Series Solution |
| title_short |
On the Effective Region of Convergence of the Decomposition Series Solution |
| title_full |
On the Effective Region of Convergence of the Decomposition Series Solution |
| title_fullStr |
On the Effective Region of Convergence of the Decomposition Series Solution |
| title_full_unstemmed |
On the Effective Region of Convergence of the Decomposition Series Solution |
| title_sort |
on the effective region of convergence of the decomposition series solution |
| publisher |
SAGE Publishing |
| series |
Journal of Algorithms & Computational Technology |
| issn |
1748-3018 1748-3026 |
| publishDate |
2013-06-01 |
| description |
In this paper we investigate the domain of convergence of the Adomian series solution based on the computational results for several examples. We demonstrate how the domain of convergence can be extended by introducing a parameter c in the definition of the zeroth-order and first-order solution components u 0 and u 1 . Furthermore we generalize the concept of the convergence parameter c from a two-term partition of the initial condition to a multiple-term partition with the design of expanding the domain of convergence of the Adomian series solutions for nonlinear differential equations. |
| url |
https://doi.org/10.1260/1748-3018.7.2.227 |
| work_keys_str_mv |
AT junshengduan ontheeffectiveregionofconvergenceofthedecompositionseriessolution AT randolphrach ontheeffectiveregionofconvergenceofthedecompositionseriessolution AT zhongwang ontheeffectiveregionofconvergenceofthedecompositionseriessolution |
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1724516582305038336 |